FIG. 1 depicts a model of an impedance measuring system. A signal source E, a device under test (DUT) Z.sub.X, and measuring instruments M1, M2 are connected to an intermediating network (transducer TRD). The DUT's impedance is determined by a function (bilinear transformation) of two measured values (e.g., complex voltages or currents) at internal points of the TRD. The difference between impedance measurement by the conventional reflection coefficient and voltmeter/ammeter (V-I) methods is merely in the TRD network and the two measuring points. That is, the difference is in the coefficients of the following bilinear transformation formula: EQU Z.sub.X =a (1+br)/(1+cr) (1)
where r=V.sub.1 /V.sub.2 (V.sub.1 and V.sub.2 indicate values measured by the measuring instruments M1 and M2, respectively). Symbols a, b, c are coefficients determined by the type of transducer, and are based on a ratio of measured values when the connection end to be connected with Z.sub.X (measurement port) is connected to a short circuit, open circuit, and 50.OMEGA. load, respectively. The type of network used for the TRD is determined in accordance with the desired impedance measurement range and the desired measurement frequency range.
FIG. 2 is a schematic diagram of a high-frequency impedance measuring apparatus in accordance with the model of FIG. 1. A signal source is connected to the TRD, and measuring instruments V.sub.1, V.sub.2 are connected to the TRD by extension coaxial cables having a characteristic impedance Z.sub.0 (Z.sub.0 =R.sub.0). Signal regulators adjust the relationship between the input signal and the full-scale outputs of the measuring instruments (ranging action).
Temperature stability and measurement S/N are factors that adversely influence measuring performance. In the FIG. 2 apparatus, temperature stability is affected by the temperature sensitivity of the TRD network and the complex gain of the measuring instrument. The gain variation of the measuring instrument is mainly caused by the transmission gain change of the extension cable and the gain change of the voltmeter. The measurement S/N is affected by instrument S/N. If the signal regulator is properly set, the instrument S/N is obtained as a dynamic range of the voltmeter, i.e., a ratio of a full-scale value to a zero-point error (noise or offset).
The measurement performance of a conventional high-frequency impedance measuring apparatus will now be considered. FIG. 3 is a schematic diagram for explaining the reflection coefficient measuring method. Commercially available impedance meters having a 1 MHz to 1 GHz frequency range employ this method. A resistor bridge 1 is employed as a transducer, or TRD, a voltage of a signal source corresponding to an input voltage is measured, and an unbalance voltage of the bridge corresponding to the reflection voltage is measured. The impedance of the DUT is calculated by using the ratio of the reflection and input voltages (reflection coefficient). The signal source 3, measuring instruments 4, 5 and bridge 1 are connected with coaxial cables 2 (measuring instrument extension cables).
The unknown impedance Z.sub.x is expressed by the following equations: EQU Z.sub.x =a (1+br)/(1+cr) (a=R.sub.0, b=1, c=-1) EQU Z.sub.x =R.sub.0 (1+r)/(1-r),
r (reflection coefficient)=8 V.sub.r /V.sub.i
A detailed circuit is described in Japanese Patent Publication No. 64-1748.
FIG. 5 depicts a characteristic relationship between values of Z.sub.x and an error expansion ratio associated with this measuring method. The error expansion ratio equals a Z.sub.x measuring error (%) divided by an error of the measuring instrument (for example, the measuring instrument 4, 5) (%). Assuming now that the abscissa of this graph indicates the values of Z.sub.x, and the ordinate logarithm thereof represents unbalance voltages of the bridge, the relationship between the unbalance voltages and Z.sub.x is represented as a solid line "a" based upon the above equation. The measuring apparatus pre-stores the solid line "a" and determines Z.sub.x on the basis of the measured unbalance voltage. Considering now the "temperature stability", it is assumed that the solid line "a" is changed to a dotted line "b" by variations in gains of the measuring device. Measurement error occurs since the values of Z.sub.x in solid line "a" are different from the values of Z.sub.x in dotted line "b", even if the unbalance voltages are the same.
It should be noted that, when a DUT having a real resistance value of 50.OMEGA. is measured and if the temperature stability of the bridge (TRD) itself is improved, variations in the gain of the measuring instruments cause a small variation in the measured values of the impedance. That is because the unbalance voltage of the bridge represents a shift from 50.OMEGA., and this unbalance voltage is very small when the DUT impedance is near 50.OMEGA.. However, as shown in FIG. 5, the temperature coefficient of the gains of the measuring instrument is greatly expanded during a measurement of a DUT impedance other than the characteristic impedance. For instance, with respect to the measurements of 500.OMEGA. or 5.OMEGA., the gain variation in the measuring instrument is expanded 10 times (a ratio of 500.OMEGA. to 50.OMEGA.), which may cause changes in the measured values. In other words, a variation of 1% in the gains of the measuring instrument may cause an error of 10% in the measurement.
The "measured S/N" is similar to the case of the above-described measurement. If the measuring instrument includes a signal regulator, then the instrument S/N remains constant, independent of the DUT impedance. However, the measured S/N is considerably deteriorated when the DUT impedance is not 50.OMEGA.. It should be noted that there is no difference in the DUT measurement errors caused by variations in the cable characteristics and the gains of the measuring instrument; this holds even when the cable at the measuring port side of the TRD is extended and the cable at the measuring instrument side is extended.
FIG. 4 is a schematic diagram of a conventional voltmeter/ammeter (V-I) measuring apparatus. V-I impedance meters having a frequency range of up to 100 MHz are commercially available. The signal source 3, measuring instruments 4, 5 and DUT (Z.sub.x) are connected to each other via coaxial cables 2, and the current flowing through the DUT is detected by the measuring instrument 4 via a current transformer 6 having a winding ratio of 1:N, which floats a current measuring point. That is, the current flowing through the DUT is measured by the current transformer 6 as a first measured value, and a voltage across the DUT, which also includes a voltage drop across the current transformer, is measured as a second measured value. The impedance of the DUT is calculated from a ratio of these two measured values. An unknown impedance Z.sub.x is calculated with the following formula: EQU Z.sub.x =a (1+br)/(1+cr) (ab=R.sub.0, b=.infin., c=0) EQU Z.sub.x R.sub.0 .multidot.r,
r=V.sub.v /V.sub.i
Considering temperature stability, if both a voltage and a current produced in the DUT can be measured under an ideal condition (which is described below), the temperature coefficient of the gains in the measuring instrument will not be expanded. Any changes in the gains of the measuring instrument appear as changes in measured impedance values with a 1:1 relationship, approximately. For instance, a variation of 1% in the gains of the measuring instrument may cause approximately 1% error in the measured values. This condition is shown in FIG. 6. Similar to the measured S/N, if the measuring instrument includes a signal regulator, a ratio of the measured S/N to the instrument S/N corresponds to about 1:1, and does not depend upon the DUT impedance.
It should be understood that, in the V-I method, there is a difference between the influences on the measurement errors due to the changes in the cable characteristics and changes in the gains of the measuring instruments in a case where the cable is extended at the measuring port side via the TRD and in a case where the cable is extended at the measuring instrument side. The cable extension at the measuring instrument maintains the error expansion ratio shown in FIG. 6, whereas the measurement error other than the characteristic impedance of the cable may be greatly enlarged by the cable extension at the side of the measuring port. This may be considered since an "ideal open" and "ideal short circuit" are difficult to realize (these ideal circuits are described below). As a consequence, since the extension of the measuring port reduces the merit of the V-I method, the cable extension is usually performed at the measuring instrument side.
The above mentioned "ideal" condition implies that the conditions V.sub.i =0 (measured current value 0, measured voltage value=finite value) and V.sub.v =0 (measured voltage value=0, measured current value=finite value) are simultaneously satisfied with the DUT under open and short circuit conditions. It is impossible to satisfy these conditions by employing two measuring instruments having finite input impedances. They can only be satisfied if at least one of the two measuring instruments can provide input impedances from zero to an infinite value.
FIG. 7 is a schematic diagram of "a circuit to achieve an ideal open measurement," and FIG. 8 is a schematic diagram of "a circuit to achieve an ideal short circuit measurement." Reference numeral 10 denotes a signal source; reference numeral 12 denotes a voltmeter; and reference numeral 14 denotes an ammeter. In the non-ideal V-I method by which the ideal open measurement and the ideal short circuit measurement cannot be obtained, variations in the gain of the measuring instrument cause influences on the measured impedance values; these influences may be effected while maintaining the error expansion ratio similar to the above-described reflection coefficient method, depending upon the degrees. In other words, in a circuit where the ideal open condition can be achieved and the ideal short circuit condition cannot be achieved, the error expansion ratio becomes large in the low impedance region, whereas in a circuit where the ideal short circuit condition can be achieved and the ideal open condition cannot be achieved, the error expansion ratio becomes large in the high-impedance region.
In the circuit shown in FIG. 4, the circuit to achieve an ideal open measurement (FIG. 7) is used as the basic circuit. A current transformer 6 having a winding ratio of 1:10 is used to realize the circuit to achieve an ideal short circuit measurement. The current transformer 6 lowers the input impedance of the measuring instrument 4 for measuring the current (the input impedance is reduced by a factor of 1/N.sup.2). However, use of the current transformer presents the following drawbacks:
(a) The larger the winding ratio is increased to realize the ideal short circuit measurement, the smaller the signal derived from the TRD becomes (the signal is reduced by a factor of I/N). The measurement S/N for measuring the impedance of a high impedance DUT is reduced.
(b) It is difficult to construct a transformer with a broad frequency band. This item is discussed below in paragraphs c, d, e.
(c) It is difficult to set the primary/secondary coupling degree to a large value over a broad frequency band (this requires reducing the leakage reactance); it is also difficult to maintain a high exciting impedance. It is not possible to use a multi-winding-to-one transformer operated at 1 MHz, for instance, under 1 GHz, taking account of variations in the magnetic permeability, a leakage inductance of a secondary winding, and a distributed capacitance.
(d) If a transformer designed for low-frequency operation is used, the ideal open measurement value and the ideal short circuit measurement cannot be reduced to an expected small value in a high frequency region. This is because, when the core size of the transformer is increased, the primary residual inductance is increased and the capacitance between the primary winding and the core is increased.
(e) Since a value of the exciting impedance in the low frequency region is mainly dependent upon the magnetic permeability of the core, the temperature characteristic of the core may cause variations in the measurement gains and the primary residual impedances.
Now, let's consider the circuit to achieve the ideal open measurement and the circuit to achieve the ideal short circuit measurement from a different point of view. FIG. 9 is a general characteristic diagram of the circuit to achieve the ideal open measurement shown in FIG. 7. In this figure, the abscissa represents an impedance and the ordinate represents the logarithm of a measured value (with respect to a certain regulated value). In a region where the impedance is large, the variation in values of current (I, V.sub.i) through the DUT is large. On the other hand, FIG. 10 is a general characteristic diagram of a circuit to achieve the ideal short circuit measurement. In this case, in a region where the impedance is small, a variation in values of voltage (V, V.sub.v) across the DUT is large. Accordingly, if the circuit to achieve the ideal open measurement is employed during the high impedance measurement and the circuit to achieve the ideal short circuit measurement is utilized during the low impedance measurement, a measurement with high sensitivity can be achieved over a broad impedance range. FIGS. 9 and 10 are practically characteristic diagrams of a circuit shown in FIG. 19.
The merits and demerits of the reflection coefficient method and the V-I method will now be summarized.
The reflection coefficient method is suitable for measuring impedances near the characteristic impedance of the bridge (for example, 50.OMEGA.). However, the precision (stability, measurement S/N) of this method is greatly lowered when impedances other than 50.OMEGA. are measured over a wide impedance range, stable precision can be achieved with the V-I method. If the signal regulator is assembled into the measuring instrument, the measured S/N becomes stable. This method is remote-measurable. However, with the conventional V-I method, it is difficult to improve the measured S/N, simultaneously achieve the ideal open measurement as well as the ideal short circuit measurement, and also broaden the frequency range. Furthermore, it is rather difficult to expect the better temperature characteristic of the broadband current transformer employed in the conventional V-I method.